Inverse Trigonometric Functions
NCERT Class 12
CBSE
Grade 12
Question:
Express $\tan^{-1}\left(\dfrac{x}{\sqrt{a^2 - x^2}}\right)$, $|x| < a$ in the simplest form.
Step-by-Step Solution
Let $x = a \sin \theta \Rightarrow \text{Argument} = \dfrac{a \sin \theta}{a \cos \theta} = \tan \theta$. [1.0 Mark]
$\tan^{-1}(\tan \theta) = \theta = \sin^{-1}(x/a)$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Substituting $x = a\sin\theta$: 1.0 Mark
Evaluating simplest form $= \sin^{-1}(x/a)$: 1.0 Mark
Correct Answer:
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